As a statement the sentence would be The primary cause and the primary consequence of the ... are ... , and not The primary cause and the primary consequence of the ... is ... It follows that if the subject is to be coordinated, the question must be as in your first sentence. The only way you could make it shorter would be by writing it as the not altogether satisfactory What are the primary cause and consequence of the ...? Your third sentence is also grammatical, because each clause has a singular subject and a singular verb.

A singular verb is also possible when a coordinated subject is a notional singular, as in What is the primary cause and basis of the ...?